Digital SATMath: Advanced MathMedium
A civil engineer is calculating the stress on a bridge support. The stress S (in Pascals) at a certain point is given by the expression (x^2 - 9) / (x^2 - 5x + 6). For what value(s) of x is the expression undefined?
- Ax = -3 and x = 2
- Bx = 3 only
- Cx = 2 and x = 3
- Dx = 2 only
Show answer & explanationAnswer & explanation
Correct answer: C. x = 2 and x = 3
An expression is undefined when its denominator is equal to zero. Factor the denominator x^2 - 5x + 6 to find the values of x that make it zero.
Why the other options are wrong
- A. Incorrect, x=-3 does not make the denominator zero; it's a root of the numerator.
- B. Incorrect, x=2 also makes the denominator zero.
- D. Incorrect, x=3 also makes the denominator zero.
Domain of Rational Functions
The set of all possible input values (x-values) for which a rational function is defined. For rational functions, the denominator cannot be zero.
- Rational functions are ratios of two polynomials.
- The function is undefined when the denominator is zero.
- Exclude values of x that make the denominator zero from the domain.
Memory trick: Denominator zero, expression no go!